Activation gaps of fractional quantum Hall effect in the second Landau level

Abstract

We present activation gap measurements of the fractional quantum Hall effect (FQHE) in the second Landau level. Signatures for 14 (5) distinct incompressible FQHE states are seen in a high- (low-) mobility sample with the enigmatic $5∕2$ even-denominator FQHE having a large activation gap of $\ensuremath{\sim}500$ $(\ensuremath{\sim}250)\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ in the high- (low-) mobility sample. This is the largest gap ever reported for the $5∕2$ FQHE state. Our measured large relative gaps for $5∕2$, $7∕3$, and $8∕3$ FQHEs indicate the emergence of exotic FQHE correlations in the second Landau level, possibly different from the well-known lowest-Landau-level Laughlin correlations. Our measured $5∕2$ gap is found to be in reasonable agreement with the theoretical gap once finite-width and disorder-broadening corrections are taken into account.